The plenacoustic function, sampling and reconstruction

In the present paper, we study the spatialization of the sound field in a room, in particular the evolution of room impulse responses as function of their spatial positions. The presented technique allows us to completely characterize the sound field in any arbitrary location if the sound field is known in a certain finite number of positions. The existing techniques usually make use of room models to recreate the sound field present at some point in the space. Our technique simply starts from the measurements of impulse responses in a finite number of positions and with this information the total sound field can be recreated. An analytical solution of the problem is given for different cases of spaces. Further, we determine the number and the spacing between the microphones needed to perfectly reconstruct the sound field up to a certain temporal frequency. The optimal sampling pattern for the microphone positions is given. Applications are also discussed.